Both are names that are common in Crypto space. And people seem to misunderstand the concept or get confused when they are both promoted/discussed.
Permissionless is not Zero Permission... it simply is "Permission is Less". Same as Trustless - It is not Zero Trust... It simply is "Trust is Less"
✴ Let's Apply both Concept to a Decentralized Christain Community/Forum to Help You Understand Them more:
Assuming such Community or Forum exists and new people want to join, they are allowed to join with small/verylittle Permission (maybe they just need to click few things, solve puzzles, register with only name & password etc) and they join automatically. The Permissionless applies as long as the new members do not break any serious/important rules of the Community. If they do, they will be suspended from the community, and may now be require to go through more Permission to ever be able to post or use the forum again.
Same applies to Trustlessness. The Community/Forum doesn't need to apply too much Trust for interested people who wish to join... We assume they are going to be good members of the community. But they will probably need to be Brandnew users of the whole Decentralized Network (no bad or good reputation), or have fair reputation "score" from other good Communities within the Decentralized Network.
The Trustlessness applies as long as the new members do not break any serious/important rules of the Christian Community. If they do, they will be suspended from the community, and will now require more Trust to ever be able to post or use the forum again.
This^ mostly is how truely Decentralized Networks/Systems (which includes decentralized apps) should operate.
✴ However, Trust and Permission could increase for people with lots of responsibilities on Decentralized Networks /Systems... People who wish to be entrusted with lots of responsibilities could be required to have consistently good records, reputations, merits, morals, etc. Their real private information (such as, home address, full names, DoB, Nationality etc) could aswell be used/staked.
Such Private info should be encrypted/hidden for the sake of the security/safety of the owners. It will be unwise/dangerous to expose people's private information to people who could abuse/misuse them. It's either people with strong morals, (trusted mostly by trusted/moral members of the community) should transparently verify and get the private info encrypted/hidden OR you just assume that no one can be trusted, and instead get multiple people with good reputation to verify and encrypt different parts of the info. The encrypted Private Information will need to be held(securely) on shared/decentralized network.
If you understand/see Trustlessness or Permissionless this way^, the confusion will reduce and you will know that both concepts are good and natural to mankind.
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✳Edit:
Added⏬ (11/9/2020)
Related Post:Permissionless/Trustless or Permission-minimized/Trust-minimized
https://bitcointalk.org/index.php?topic=5287793.msg55551891#msg55551891
